Hessian-free force-gradient integrators
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915096515575808 |
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| author | Schäfers, Kevin Finkenrath, Jacob Günther, Michael Knechtli, Francesco |
| author_facet | Schäfers, Kevin Finkenrath, Jacob Günther, Michael Knechtli, Francesco |
| contents | We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10370 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hessian-free force-gradient integrators Schäfers, Kevin Finkenrath, Jacob Günther, Michael Knechtli, Francesco Numerical Analysis High Energy Physics - Lattice Mathematical Physics 81V05, 65P10, 65L05, 65L20 37N20 We propose a new framework of Hessian-free force-gradient integrators that do not require the analytical expression of the force-gradient term based on the Hessian of the potential. Due to that the new class of decomposition algorithms for separable Hamiltonian systems with quadratic kinetic energy may be particularly useful when applied to Hamiltonian systems where an evaluation of the Hessian is significantly more expensive than an evaluation of its gradient, e.g. in molecular dynamics simulations of classical systems. Numerical experiments of an N-body problem, as well as applications to the molecular dynamics step in the Hybrid Monte Carlo (HMC) algorithm for lattice simulations of the Schwinger model and Quantum Chromodynamics (QCD) verify these expectations. |
| title | Hessian-free force-gradient integrators |
| topic | Numerical Analysis High Energy Physics - Lattice Mathematical Physics 81V05, 65P10, 65L05, 65L20 37N20 |
| url | https://arxiv.org/abs/2403.10370 |